Monday, 5 September 2011

GOD

Note on Conjoint AnalysisOrthographic projection (or orthogonal projection) is a means of representing a three-dimensional object in two dimensions. The term orthographic is also sometimes reserved specifically for depictions of objects where the axis or plane of the object is also parallel with the projection plane.

The Principle of Orthogonal Design (abbreviated POOD) is a principle of database design, which seek to prevent databases from being too complicated or redundant. Simply put, it says that no two relations in a relational database should be defined in such a way that they can represent the same facts. As with database normalization, POOD serves to eliminate uncontrolled storage redundancy.

Generate Orthogonal Design generates a data file containing an orthogonal main-effects design that permits the statistical testing of several factors without testing every combination of factor levels. This design can be displayed with the Display Design procedure, and the data file can be used by other SPSS procedures, such as Conjoint.

To reduce the levels of option available, we select profiles more efficiently. One of the most common experimental designs is known as an orthogonal fractional factorial design – an “orthogonal design” for short. Such designs are conceptually similar to the popular Sudoku puzzles where players are asked to place the numbers 1 through 9 in a grid such that no number appears twice in a row, in a column, or in a 3x3 sub-box. In an orthogonal design, the levels of the features are chosen such that, for each pair of features, say a and b, the high level a appears equally often in profiles that have a high level b as in profiles that have a low level of b, and vice versa. Such experimental designs are extremely efficient for estimating part worth for features. These designs do not come without a cost. They confound “interactions.” For example, with such designs we can only estimate “main effects” of each feature. This is equivalent to an assumption that the part worth of having high levels of both a and b equals the part-worth of a high level of a plus the part worth of a high level of b. If there were an interaction, the value of having high levels on both a and b might by synergistically more valuable than the value of having a high level of a and the value of having a high level of b.Orthogonal designs are not the only fractional factorial designs. We can create designs that require more profiles, but which allow us to estimate some interactions. The study of experimental designs is beyond the scope of this note. However, it is useful to illustrate an orthogonal design for 16 features that requires only 32 profiles.